Question

Find th altitude of a parallelepiped whose three coterminous edges are vectors `vecA=hati+hatj+hatk,vecB=2hati+4hatj-hatkand vecC=hati+hatj+3hatk "with" vecA and vecB` as the sides of the base of the parallelepiped .

Answer 1

`h=("volume of parallelepiped")/("Area of base")`
`=([vec(A)vec(B)vec(C)])/(|vec(A)xxvec(B)|)=(|(1,1,1),(2,4,-1),(1,1,3)|)/(|(hat(i),hat(j),hat(k)),(1,1,1),(2,4,-1)|)=(4)/(|-5hat(i)+3hat(j)+2hat(k)|)=(2sqrt(38))/(19)`